相关论文: Global and Local Topological Quantized Responses f…
Topologically ordered states are quantum states of matter with topological ground state degeneracy and quasi-particles carrying fractional quantum numbers and fractional statistics. The topological spin $\theta_a=2\pi h_a$ is an important…
Based on Haldane's spherical geometrical formalism of two-dimensional quantum Hall fluids, the relation between the noncommutative geometry of $S^2$ and the two-dimensional quantum Hall fluids is exhibited. If the number of particles $N$ is…
We present mathematical details of the construction of a topological invariant for periodically driven two-dimensional lattice systems with time-reversal symmetry and quasienergy gaps, which was proposed recently by some of us. The…
Topological insulators are novel macroscopic quantum-mechanical phase of matter, which hold promise for realizing some of the most exotic particles in physics as well as application towards spintronics and quantum computation. In all the…
A local realistic model for quantum mechanics of two-particle Einstein-Podolsky-Rosen pairs is proposed. In this model, it is the strict obedience of conservation laws in each event at the quantum level that uphold the perfect correlation…
We employ the Dirac procedure to quantize the self-dual massive Kalb-Ramond-Klein-Gordon model in $2+1$ dimensional spacetimes. The canonical fields are expressed in terms of $2$-surfaces and signed points, ensuring the automatic…
The concept of electric and magnetic field lines is intrinsically non-relativistic. Nonetheless, for certain types of fields satisfying certain geometric properties, field lines can be defined covariantly. More precisely, two…
We calculate a topological invariant, whose value would coincide with the Chern number in case of integer quantum Hall effect, for fractional quantum Hall states. In case of Abelian fractional quantum Hall states, this invariant is shown to…
The Haldane model on the honeycomb lattice is a paradigmatic example of a Hamiltonian featuring topologically distinct phases of matter. It describes a mechanism through which a quantum Hall effect can appear as an intrinsic property of a…
We have recently identified a protected topological semimetal in graphene which presents a zero-energy edge mode robust to disorder and interactions. Here, we address the characteristics of this semimetal and show that the $\mathbb{Z}$…
We construct a topological ladder model, one-dimensional, following the steps which lead to the Kane-Mele model in two dimensions. Starting with a Creutz ladder we modify it so that the gap closure points can occur at either $k = \pi / 2$…
Quantum systems are often described by parameter-dependent Hamiltonians. Points in parameter space where two levels are degenerate can carry a topological charge. Here we theoretically study an interacting two-spin system where the…
We discuss some aspects of topological invariants that classify topological states of matter with emphasis on topological insulators. The main aspect addressed is if there are only two topological phases to Bloch Hamiltonian that are time…
There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in the space of constant positive curvature, spherical Riemann space, in presence of an external magnetic field, analogue of the…
We discuss the topological phase transition of the spin-$\frac{1}{2}$ fermionic Haldane model with repulsive on-site interaction. We show that the Berry curvature of the topological Hamiltonian, the first Chern number, and the topological…
The recently introduced classification of two-dimensional insulators in terms of topological crystalline invariants has been applied so far to "obstructed" atomic insulators characterized by a mismatch between the centers of the electronic…
There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in Riemannian space of constant negative curvature, hyperbolic Lobachevsky space, in presence of an external magnetic field, analogue…
Topological systems, such as fractional quantum Hall liquids, promise to successfully combat environmental decoherence while performing quantum computation. These highly correlated systems can support non-Abelian anyonic quasiparticles that…
We show there are analogues to the Unruh temperature that can be defined for any quantum field theory and region of the space. These local temperatures are defined using relative entropy with localized excitations. We show important…
We study responses to metric perturbation in topological insulator models. In this paper we introduce a novel quantity, Hall viscosity to particle density ratio, which is analogous to the viscosity to entropy ratio suggested by AdS/CFT…